Problem: Reduce to lowest terms: $- \dfrac{7}{6} \div \dfrac{4}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{4}{3}$ is $ \dfrac{3}{4}$ Therefore: $ - \dfrac{7}{6} \div \dfrac{4}{3} = - \dfrac{7}{6} \times \dfrac{3}{4} $ $ \phantom{- \dfrac{7}{6} \times \dfrac{3}{4}} = \dfrac{-7 \times 3}{6 \times 4} $ $ \phantom{- \dfrac{7}{6} \times \dfrac{3}{4}} = \dfrac{-21}{24} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-21}{24} = \dfrac{-21 \div 3}{24 \div 3} = -\dfrac{7}{8} $